Math CentralQuandaries & Queries


Question from prateet, a student:

in an equilateral triangle prove that the centroid and centre of the circumcircle coincide

here i am not clear about the concept of centroid and circumcircle
i cant understand how AGis 2/3 AD.
please help in details about the topic mentioned.


You can look in our glossary for a definition of the centroid of a triangle and circumcentre of a triangle. You have an equilateral triangle and the symmetry in this triangle is very useful in working with the centroid and circumcircle.


In my diagram L, M and N are the midpoints of the respective sides. C is the centroid. To show it in the circumcentre you need to show that |CP| = |CQ| = |CR|.

By the symmetry the line segment RN bisects the angle QRP. What is the measure of angle NRP? Again by the symmetry the 6 angles at C have the same measure. What is the measure of the angle MCR? What does this tell you about the triangle MCR?

Does this help?

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